Model studies of blood flow in basilar artery with 3D Laser Doppler
Anemometer
Frolov S.V.1, Sindeev S.V.1, Liepsch D.2, Balasso A.3, Proskurin S.G.1, Potlov A. Yu1,
1
2
– Tambov State Technical University, Tambov, Russia
– Munich University of Applied Sciences, Munich, Germany
3
– Technical University of Munich, Munich, Germany
One of the most common disorders of cerebral circulation is an aneurysm of
the basilar artery. Damage of the vessel wall is caused by local hemodynamics
disorders; therefore, the study of basilar artery hemodynamics plays a key role in
identifying the causes of the emergence and development of the aneurysm [1].
Mathematical model. For the investigation of basilar artery circulation it is
proposed to use a multiscale mathematical model of hemodynamics [1], which is a
set of mathematical models of circulation with different levels of detail.
It is proposed to develop a 0D model to describe all major compartments of
cardiovascular system and to describe heart in terms of physiology.
Developing the one-dimensional hemodynamics (1D model) model of arterial
tree it is planned to describe upper body arteries as a set of quasi-one-dimensional
vessels. This model allows studying the phenomenon of pulse wave propagation
through the arterial tree, and to identify and predict the possible disorder in the
functioning of the arteries.
Using 3D model it is planned to describe the basilar artery local
hemodynamics. The researcher will receive information about a blood flow rate of
change and blood pressure at any point of the basilar artery. According to results risk
of developing an aneurysm of the basilar artery can be predicted. Also, with this
model it is possible to conduct numerical experiments to determine the optimal stent
position in basilar artery stenting.
3D model is developed using the Navier-Stokes equations [2]. Blood flow rate
and pressure are studied functions. Unlike 1D model studied functions vary in three
1
spatial directions, causing a significant increase in simulation time for this type of
models.
Thus, a correct modeling of the investigated arterial segment (basilar artery)
requires development of a set of interrelated models 0D, 1D and 3D, which together
form a multiscale mathematical model of the hemodynamics of the cardiovascular
system [1].
This model allows to combine models of the global hemodynamics, arterial
tree hemodynamics and local hemodynamics of basilar artery that takes advantage of
each type of model and minimize their weaknesses. For example, a multiscale model
of hemodynamics has an opportunity to study the impact of regulation (0D model) at
the local segment of cardiovascular system (3D model).
Experimental set-up. The experimental set-up is shown in Fig. 1. With 3D
laser-Doppler-anemometry it is possible to measure the velocity distribution of a flow
with high spatial (70µm) and temporal (1ms) resolution in transparent models of
human vessels without disturbing the flow [3] [4].
The silicone rubber models used to provide transparent, true-to-scale replicas of
human vessels. To obtain geometry data of patients, digital images from the MRI or
CT are segmented. Using a stereolithography method plastic model forms are made
from these images. This first model forms are used to create silicone tube, in which
vascular models from wax are produced.
The wax cores are the basis for casting the silicone tubes. First is applied to the
cores, a separating agent layer, in order to avoid a direct contact of silicone wax.
After drying of the core it may be immersed in the silicone bath, so that is a first thin
layer. The coated wax core is allowed to dry for several hours. Then it is again dipped
in the prepared silicone mixture. In this way as many layers as needed applied to the
wax cores. The models are heated in an oven to melt the wax core. In this way, the
wax can leak out of the silicone rubber model. After this a silicone rubber model is
cleaned and dried after completion.
The vessel’s model is mounted on an x-y-z-moving table so that velocities can be
measured and recorded very precisely at each point of interest. In order to obtain a
2
representative picture of the flow, velocity is measured by 3D LDA at each point for
seven pulse cycles and then averaged [5] [6] [7].
To simulate the physiological human flow conditions we use a blood-like fluid
developed in our laboratory. The perfusion fluid is a transparent glycerol-water
mixture to which is added a small amount of Separan AP-302 and Separan AP-45
(Dow Chemical). This fluid exhibits a non-Newtonian flow behavior similar to that of
blood.
1 Piston pump
2 Elevated tank
3 Overflow tank
4 Personal Computer
5 3D LDA
6 Сollecting tank
7 Buffer tank
8 Flow transducer
9 Pressure transducer
10 Basilar artery model
11 Regulation tanks
12 Buffer tank
13 Flow meter
14 Photommultiplier
Fig 1. Experimental set-up
The perfusion fluid is pumped from a collecting tank (6 in Fig. 1) through an
elevated tank (2 in Fig. 1) into an overflow tank (3 in Fig. 1). It maintains a constant
static pressure in the model. A computer driven piston pump (1 in Fig. 1)
superimposes an oscillatory pulse on the stationary flow creating a pulsatile flow.
Buffer tanks (7, 12 in Fig. 1) are installed in front and behind of the model to
simulate the compliance of a human aorta. The fluid streams through the model (10 in
Fig. 1) back into the collecting tank (6 in Fig. 1). Regulation tanks (11 in Fig. 1)
3
allow an adjustment of the flow rate. Pressure is measured with inductive pressure
transducers (9 in Fig. 1). Systolic and diastolic pressure can be set in the range
between 150 mmHg and 70 mmHg.
Velocity, pressure and flow rate data obtained with the above described
experimental set-up allow to correlate with the mathematical simulation in order to
evaluate its reliability. The aim is to determine when there is a rupture of the
aneurysm, and to provide criteria to avoid a rupture. This is done through the
comparison and analysis of the experimental data with the data calculated by means
of computer simulation in a multiscale mathematical model of hemodynamics.
References
Список литературы
1. Steiger H.J., Liepsch D.W., Poll A., Reulen H.J. Hemodynamic stress in
terminal saccular aneurysms: a laser-Doppler study // Heart and Vessels. — 1988. —
Vol. 4, 3. — P. 162-169.
2. Frolov S.V., Sindeev S.V., Liepsch D., Balasso A. Mathematical modeling
of blood flow in basilar artery bifurcation region // Transactions TSTU. — 2014. —
Vol. 20, 1. — P. 50-58.
3. Frolov S.V., Sindeev S.V., Lischouk V.A., Gazizova D.Sh., LIepsch D.,
Balasso A. Development of multiscale hemodynamics model for research of basilar
artery circulation // Problems of Contemporary Science and Practice. Vernadsky
University. — 2013. — Vol. 48, 4. — P. 46-53.
4. Liepsch D. An introduction to biofluid mechanics - basic models and
applications // Journal of Biomechanics. — 2002. — 35. — P. 415-435.
5. Mijovic B., Liepsch D. Experimental flow studies in an elastic Y-model //
Technology and Health Care. — 2003. — Vol. 11, 2. — P. 115-141.
6. Liepsch D. Fundamental flow studies in models of human arteries //
Frontiers of Medical & Biological Engineering. — 1993. — Vol. 5, 1. — P. 51-55.
4
7. Poll A., Liepsch D., Weigand C., McLean J. Two an dthree-dimensional
LDA measurements and shear stress calculations for a true-to scale elastic model of a
dog aorta with stenosis // Automedica. — 2000. — Vol. 18. — P. 163-210.
5